This article deals with a complete normed field K, a Banach space V over K, a Banach Lie group G over K, its Lie algebra \(\hat G,\) the Spencer homologies \(H^{i,j}(\hat G)\) and the Cartan manifold \(Cart(V,\hat G)\subset H^{0,2}(\hat G).\) The main result is the existence of a quasi-homogeneous G-structure with given structure constants \(c\in Cart(V,\hat G)\) in the case when \(H^{i,j}(\hat G)=0\) (i\(\geq 0\), \(0\leq j\leq 3)\) and K is ultrametric. In the case when \(K={\mathbb{R}}\) this result is not true but it can be considered a generalization of the third Lie theorem. For the case when \(K={\mathbb{R}}\) and V is a separable Banach space it is proved that the corresponding G-structure is homogeneous if and only if either dim \(V\leq 2\) or dim V\(=\infty\).